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Preventing Small Global Cuts by Protecting Edges

Authors Christian Komusiewicz , Zhenwei Liu , Nils Morawietz , Frank Sommer

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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Network interdiction
  • NP-hard problem
  • parameterized complexity
  • structural parameterization
  • edge-weighted graphs

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Abstract

The minimum cut problem is one of the oldest and most fundamental optimization problems in operations research. In this problem, we are given a connected edge-weighted graph (G,ω) and have to find an edge set A (called edge-cut) of smallest total weight such that the removal of the edges of A disconnects G. The problem thus takes the view of an attacker that wants to destroy the global connectivity of the network. Bienstock and Diaz [SICOMP '93] introduced Global Cut Prevention, a two-player version of the minimum cut problem where a defender aims to protect edges to increase the weight of the minimum cut of the resulting graph. More precisely, the input contains an additional edge cost function c that is independent of the attacker weight ω and the defender aims to protect an edge set of total cost at most d such that every edge-cut consisting of unprotected edges has weight at least a+1. We initiate the study of the parameterized complexity of Global Cut Prevention. Here, we consider the most natural parameters such as the budgets d and a of the players, the vertex cover number and treewidth of the input graph, and combinations of these parameters. We show, for example, that the encoding of the costs and weights of the edges has a considerable influence on the problem complexity: If each edge has unit defender cost and unit attacker weight, then Global Cut Prevention is FPT for the vertex cover number. If the attacker weights are arbitrary and encoded in unary, then the problem is W[1]-hard for the vertex cover number but still admits an XP-algorithm. Finally, if the defender cost and the attacker weight are encoded in binary, then the problem becomes NP-hard even on graphs with a vertex cover of size 2.

Cite As Get BibTex

Christian Komusiewicz, Zhenwei Liu, Nils Morawietz, and Frank Sommer. Preventing Small Global Cuts by Protecting Edges. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WG.2026.30

Author Details

Christian Komusiewicz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany
Zhenwei Liu
  • Zhejiang University, Hangzhou, China
Nils Morawietz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany
Frank Sommer
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany

Funding

  • Sommer, Frank: Supported by the Alexander von Humboldt Foundation.

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